Finite Group Databasebeta

← #14656381

Subgroups — #14656381

Order 2816.

574 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622312C211yesmaximal, characteristic
2C2×#10622633C212yesmaximal
3C2×#10622120C212yesmaximal
4#13066451C211yesmaximal, characteristic
5C11×#1984C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C22×Dic44—22no—
8C2×#66922C2212yes—
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66899—22no—
12#10622633—24no—
13#10622633—24no—
14C2×#66872—22no—
15C2×C4⋊(C11⋊C8)C2212yes—
16#10622312—24no—
17C11×#336—22no—
18#10622120—24no—
19C22×Q8×C11D411yescharacteristic
20C22×Dic22—22no—
21C22×C8×C11—21no—
22C22×C8×C11D412yes—
23C4×Q8×C11—22no—
24C4×Q8×C11—22no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C42×C11—21no—
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—22no—
30C2×C4⋊Dic11—22no—
31C22×C11⋊C8—22no—
32C2×Dic44—28no—
33C2×Dic44—44no—
34C2×Dic44—44no—
35#66922—22no—
36#66922—22no—
37#66922—22no—
38#66922D414yes—
39C11×C4⋊C8—22no—
40C4×C8×C11—22no—
41#66899—28no—
42#66872—28no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)D414yes—
45#10276—111nomaximal, Sylow
46C2×Q8×C11—21no—
47C2×Q8×C11—22no—
48C2×Q8×C11—22no—
49C2×Q8×C11Q1612yescomplemented
50C22×C4×C11—21no—
51C22×C4×C11—21no—
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C22×Dic11—42no—
56C2×Dic22—24no—
57C2×Dic22—42no—
58C2×Dic22—44no—
59C2×Dic22—44no—
60C2×C8×C11—22no—
61C2×C8×C11—22no—
62C2×C8×C11—41no—
63C2×C8×C11—42no—
64C2×C8×C11SD1614yes—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—42no—
67C42×C11—41no—
68C42×C11—41no—
69C42×C11C2×D412yes—
70C42×C11C2×D412yes—
71C4⋊Dic11—24no—
72C4⋊Dic11—24no—
73C4⋊Dic11—42no—
74C4⋊Dic11—42no—
75C2×C11⋊C8—24no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—42no—
78Dic44—416no—
79C2×#494—111no—
80C2×#475—112no—
81#1984D1111yescharacteristic
82C2×#332—112no—
83#1277—111no—
84C23×C11#12111yescharacteristic
85Q8×C11—24no—
86Q8×C11—42no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11—42no—
93C2×C4×C11#12012yes—
94C2×C4×C11#12011yescharacteristic
95C2×C4×C11#12112yes—
96C2×C4×C11#12711yescharacteristic
97C2×C4×C11C2×SD1612yes—
98C2×C4×C11C2×Q1611yescharacteristic
99C2×C4×C11#13511yescharacteristic
100C2×C4×C11AGL(1,ℤ/8)12yes—
101C2×C4×C11#13712yes—
102C2×Dic11—44no—
103C2×Dic11—84no—
104Dic22—48no—
105Dic22—82no—
106Dic22—82no—
107C8×C11—24no—
108C8×C11—81no—
109C11⋊C8—44no—
110C22×Q16—222no—
111C2×C4⋊Q8—112no—
112C2×C4×Q8C2×D1111yescharacteristic
113#494—224no—
114#475—224no—
115#475—224no—
116C2×#106—222no—
117C2×C4⋊C8—112no—
118C2×C4⋊C8C2×D1111yescharacteristic
119C2×#103—222no—
120C2×C4×C8C2×D1111yescharacteristic
121#336—22no—
122#332—224no—
123C22×C11#39211yescharacteristic
124C22×C11#46012yes—
125C22×C11#46711yescharacteristic
126C22×C11#47011yescharacteristic
127C22×C11#47312yes—
128C4×C11—22no—
129C4×C11—42no—
130C4×C11—81no—
131C4×C11#45012yes—
132C4×C11#45112yes—
133C4×C11#45212yes—
134C4×C11#49211yescharacteristic
135C4×C11#49611yescharacteristic
136Dic11—84no—
137C22×Q8—222no—
138C22×Q8D4411yescharacteristic
139C2×Q16—228no—
140C2×Q16—444no—
141C2×Q16—444no—
142C22×C8—21no—
143C22×C8—222no—
144C22×C8C22⋊D1112yes—
145C4⋊Q8—114no—
146C4⋊Q8—222no—
147C4⋊Q8—222no—
148C4⋊Q8—222no—
149C4×Q8—22no—
150C4×Q8—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—222no—
153C2×C4⋊C4—222no—
154C2×C4⋊C4D4411yescharacteristic
155C2×C42—21no—
156C2×C42C22×D1111yescharacteristic
157#106—228no—
158C4⋊C8—22no—
159C4⋊C8—114no—
160C4⋊C8—222no—
161#103—228no—
162C4×C8—22no—
163C2×C11#167012yes—
164C2×C11#169012yes—
165C2×C11#200111yescharacteristic
166C2×C11#201411yescharacteristic
167C2×C11#202011yescharacteristic
168C2×Q8—21no—
169C2×Q8—22no—
170C2×Q8—22no—
171C2×Q8—224no—
172C2×Q8—442no—
173C2×Q8—444no—
174C2×Q8—444no—
175C2×Q8Dic4412yescomplemented
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—442no—
179C22×C4C2×D4411yescharacteristic
180C22×C4#433911yescharacteristic
181C22×C4C2×C22⋊D1111yescharacteristic
182Q16—4416no—
183C2×C8—22no—
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—42no—
187C2×C8—224no—
188C2×C8—442no—
189C2×C8—442no—
190C2×C8#432514yes—
191C4⋊C4—22no—
192C4⋊C4—42no—
193C4⋊C4—224no—
194C4⋊C4—224no—
195C4⋊C4—442no—
196C4⋊C4—442no—
197C42—41no—
198C42—41no—
199C42D4×D1112yes—
200C42D4×D1112yes—
201C11#1027611yescharacteristic, complemented, Sylow
202C23#6698311yescharacteristic
203Q8—24no—
204Q8—42no—
205Q8—448no—
206Q8—882no—
207Q8—882no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—444no—
215C2×C4—884no—
216C2×C4#6693512yes—
217C2×C4#6693712yes—
218C2×C4#6695711yescharacteristic
219C2×C4C2×Dic4411yescharacteristic
220C2×C4#6696212yes—
221C2×C4#6699011yescharacteristic
222C2×C4#6699311yescharacteristic
223C2×C4C2×#432512yes—
224C2×C4#6700212yes—
225C8—24no—
226C8—81no—
227C8—444no—
228C22#1062257311yescharacteristic
229C22#1062264012yes—
230C22#1062272911yescharacteristic
231C22#1062275011yescharacteristic
232C22#1062275612yes—
233C4—22no—
234C4—42no—
235C4—81no—
236C4—884no—
237C4#1062234612yes—
238C4#1062235212yes—
239C4#1062265912yes—
240C4#1062267111yescharacteristic
241C4#1062269811yescharacteristic
242C2#1306798612yes—
243C2#1306811012yes—
244C2#1306962611yescharacteristic
245C2#1306970311yescharacteristic
246C2#1306973711yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1984C2
socle, prime radicalC23×C11#121
hypercenter#1984D11
hypocenterC11#10276
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
49. C2×Q8×C11Q16semidirect
175. C2×Q8Dic44semidirect
201. C11#10276semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106223122
C2×#106226332
C2×#106221202
#130664512
C11×#19842
#1027611